Question

Find the rate at which the surface area of a
sphere is changing with respect to its radius r
when r = 3 cm.

Answer 1

What is the rate of the radius change (dr/dt)?

Answer 2

If R is a constant 3, then the surface area would also be a constant value.

Answer 3

\[
A= 4 \pi r^2\\
\frac {dA}{dt}= 8 \pi r \frac {dr}{dt}=24 \pi \frac {dr}{dt}\\

\]
If you know \( \frac{dr}{dt}\), then you would know \( \frac {dA}{dt}\)

Answer 4

when r=3

Answer 5

Perhaps all that was sought was the formula for dA/dr.

Answer 6

It could be. The question must have been more precise. @douglaswinslowcooper

Answer 7

That certainly answered the question. I thought there was more to it. But after re-reading that was all that was needed. well done @eliassaab